Excitation of Quantized Longitudinal Electric Waves in a Degenerate Fermi Gas

TL;DR

This paper investigates the excitation and stability of quantized longitudinal electric waves in a degenerate Fermi gas under magnetic fields, revealing new wave modes and growth rates due to Landau quantization effects.

Contribution

It introduces a new dispersion equation for quantized waves and identifies novel wave branches absent in classical models, advancing understanding of wave behavior in quantum plasmas.

Findings

Discovery of new wave branches due to Landau quantization

Derivation of growth rates for these new wave modes

Conditions for zero sound excitation in quantized systems

Abstract

The system of electron beam - degenerate Fermi gas in a magnetic field is investigated. Instabilities of the quantized longitudinal electric waves are studied by a newly derived dispersion equation. Novel branches of longitudinal waves are found, which have no analogies without the Landau quantization. Growth rates of these new modes are obtained. The excitation of the zero sound by an electron beam is discussed and found that the quantization of the energy of electrons imposes a new condition. Furthermore, the excitation of Bogolyubov's type of spectrum by a strong electric field is considered.